If the ratio of the lengths of two sides of a triangle is 7:5 and the perimeter

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Question: If the ratio of the lengths of two sides of a triangle is 7:5 and the perimeter is 48 cm, what is the length of the longer side?

Options:

Correct Answer: 28 cm

Solution:

Let the lengths of the sides be 7x and 5x. Then, 7x + 5x = 48, which gives 12x = 48. Thus, x = 4, and the longer side is 7x = 28 cm.

If the ratio of the lengths of two sides of a triangle is 7:5 and the perimeter is 48 cm, what is the length of the longer side?

If the ratio of the lengths of two sides of a triangle is 7:5 and the perimeter is 48 cm, what is the length of the longer side?

Step 1: Understand that the ratio of the lengths of the two sides of the triangle is 7:5.
Step 2: Let the lengths of the sides be represented as 7x (for the longer side) and 5x (for the shorter side).
Step 3: Write the equation for the perimeter of the triangle: 7x + 5x = 48.
Step 4: Combine the terms on the left side: 12x = 48.
Step 5: Solve for x by dividing both sides by 12: x = 48 / 12, which gives x = 4.
Step 6: Find the length of the longer side by calculating 7x: 7 * 4 = 28 cm.

Ratio and Proportion – Understanding how to express the lengths of sides in terms of a common variable based on their ratio.
Perimeter of a Triangle – Applying the concept of perimeter to find the total length of the sides of a triangle.
Algebraic Manipulation – Solving for a variable using basic algebraic equations.